Numerical solution of a mass structured cell population balance model in an environment of changing substrate concentration

Mantzaris, Nikos V.; Liou, Jia Jer; Daoutidis, Pródromos; Srienc, Friedrich

doi:10.1016/s0168-1656(99)00020-6

Cited by 98 publications

(95 citation statements)

References 28 publications

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“…We introduce it using a relatively simple form presented by Mantzaris et al (1999). The cells are considered heterogeneous on the basis of their mass, which is used to distinguish the physiological state of cells.…”

Section: A Single-stage Single-variable Pbmmentioning

confidence: 99%

“…Currently the favoured characterisation of S is by relating it to biomass production rate via a yield coefficient, Y, as done by Mantzaris et al (1999).…”

Section: Nð0 Tþ ¼ 0 ð6þmentioning

confidence: 99%

“…For detailed derivation see Eakman et al (1966). Using a model consisting of Equations (4)- (10), Mantzaris et al (1999) carried out a number of simulations. Various forms were used to describe the growth rate, including constant, linear and quadratic growth forms.…”

Section: Nð0 Tþ ¼ 0 ð6þmentioning

confidence: 99%

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Modelling of Mammalian Cells and Cell Culture Processes

Sidoli¹,

Mantalaris

Asprey³

2004

Cytotechnology

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Mammalian cell cultures represent the major source for a number of very high-value biopharmaceutical products, including monoclonal antibodies (MAbs), viral vaccines, and hormones. These products are produced in relatively small quantities due to the highly specialised culture conditions and their susceptibility to either reduced productivity or cell death as a result of slight deviations in the culture conditions. The use of mathematical relationships to characterise distinct parts of the physiological behaviour of mammalian cells and the systematic integration of this information into a coherent, predictive model, which can be used for simulation, optimisation, and control purposes would contribute to efforts to increase productivity and control product quality. Models can also aid in the understanding and elucidation of underlying mechanisms and highlight the lack of accuracy or descriptive ability in parts of the model where experimental and simulated data cannot be reconciled. This paper reviews developments in the modelling of mammalian cell cultures in the last decade and proposes a future direction -the incorporation of genomic, proteomic, and metabolomic data, taking advantage of recent developments in these disciplines and thus improving model fidelity. Furthermore, with mammalian cell technology dependent on experiments for information, model-based experiment design is formally introduced, which when applied can result in the acquisition of more informative data from fewer experiments. This represents only part of a broader framework for model building and validation, which consists of three distinct stages: theoretical model assessment, model discrimination, and model precision, which provides a systematic strategy from assessing the identifiability and distinguishability of a set of competing models to improving the parameter precision of a final validated model. NomenclatureC ij -component i concentration in jth model compartment; R ijk -transport rate of component i into or out of compartment j from the kth source or sink compartment; N in -number of source compartments; N outnumber of sink compartments; r ijl -reaction rate of component i in compartment j in the lth i-generating or i-consuming reaction; N gen -number of reactions generating component i; N con -number of reactions consuming component i; -specific growth rate; app max -apparent maximum specific growth rate; K dspecific death rate; N v -viable cell number; N t -total cell number; D -dilution rate; -parameter; 0 -parameter; -parameter; m -cell mass; m 0 -mass of a dividing cell; t -time; N -cell number; r -single cell growth rate; S -nutrient concentration; s -nutrient concentration vector; À -cell transition rate; ppartition probability density function; Y -yield coefficient; f (m) -the division probability density function; B -coefficient for the beta distribution incorporating the gamma function; x max -vector of maximum XPS 120742 (CYTO) -ms-code CYTO853 -product element 5254543 -23 September 2004 -Newgen

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Section: A Single-stage Single-variable Pbmmentioning

confidence: 99%

“…Currently the favoured characterisation of S is by relating it to biomass production rate via a yield coefficient, Y, as done by Mantzaris et al (1999).…”

Section: Nð0 Tþ ¼ 0 ð6þmentioning

confidence: 99%

See 1 more Smart Citation

Modelling of Mammalian Cells and Cell Culture Processes

Sidoli¹,

Mantalaris

Asprey³

2004

Cytotechnology

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“…Assuming spatial homogeneity and neglecting the effects of physical environmental parameters have been the basis of most culture models [19][20][21][22][23][24][25][26][27][28][29]. This reduces the problem of simulating relevant portions of cellular activities that control the production of a product of interest.…”

Section: Existing Culture Models and Their Need For Improvementmentioning

confidence: 99%

A Framework for the Development of Integrated and Computationally Feasible Models of Large-Scale Mammalian Cell Bioreactors

Farzan

Ierapetritou

2018

Processes

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Industrialization of bioreactors has been achieved by applying several core concepts of science and engineering. Modeling has deepened the understanding of biological and physical phenomena. In this paper, the state of existing cell culture models is summarized. A framework for development of dynamic and computationally feasible models that capture the interactions of hydrodynamics and cellular activities is proposed. Operating conditions are described by impeller rotation speed, gas sparging flowrate, and liquid fill level. A set of admissible operating states is defined over discretized process parameters. The burden on a dynamic solver is reduced by assuming hydrodynamics at its fully developed state and implementation of compartmental modeling. A change in the conditions of operation is followed by hydrodynamics switching instantaneously to the steady state that would be reached under new conditions. Finally, coupling the model with optimization solvers leads to improvements in operation.

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“…is the cell number concentration (no./g) as a function of mass (m) and time (t), ) S ( v g ′ is the overall single cell growth rate at the substrate concentration (1) can be modified by (Lim et al, 2002;Mantzaris et al, 1999):…”

Section: Cell Population Dynamicsmentioning

confidence: 99%

Modeling and prediction of cell population dynamics

Lim

2005

Computer Aided Chemical Engineering

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Oscillatory yeast cell dynamics are observed in glucose-limited growth environments. Under such conditions, both glucose and the excreted product ethanol can serve as substrates for cell growth. The cell dynamics is described by a PDE (partial differential equation) system containing one PDE for the cell population and 8 ODEs for 8 substrates variations (extracellular glucose, extracellular ethanol, intracellular glucose, intracellular ethanol, exhausted oxygen, exhausted carbon dioxide, dissolved oxygen and dissolved carbon dioxide). The system is solved by the numerical method of characteristics (MOC) modified (Lim et al., 2002). Here, mesh points are added at the smallest cell size and also deleted at the largest cell size at the same time level. The modified MOC provides a solution free of numerical dissipation error caused by the cell growth term (i.e., convection term), owing to the mass axis moving along a cell growth pathline. The oscillatory behavior of the cell number and the cell mass is predicted from the simulation. The cell number variation affects the extracellular glucose/ethanol and oxygen/carbon-dioxide concentrations in the gas exhaust stream. As ethanol is excreted primarily by budded cells, it is shown for the extracellular ethanol concentration to slowly reach a regular oscillatory state. Dynamics of the evolved oxygen concentration ratio and carbon-dioxide concentration ratio are also shown.

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Numerical solution of a mass structured cell population balance model in an environment of changing substrate concentration

Cited by 98 publications

References 28 publications

Modelling of Mammalian Cells and Cell Culture Processes

Modelling of Mammalian Cells and Cell Culture Processes

A Framework for the Development of Integrated and Computationally Feasible Models of Large-Scale Mammalian Cell Bioreactors

Modeling and prediction of cell population dynamics

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